Conventional frequency synthesizers such as phase-locked loops accomplish the generation of many different frequencies from one or more stable sources by means of an analog circuit or by a combination of analog and digital circuits. In these approaches, a generation of frequencies is performed in the analog or continuous sense by division, phase lock, mixing or some combination of these techniques.
A conventional numerically controlled oscillator (NCO) uses time domain amplitude samples to generate a sinusoidal waveform whose frequency is controlled by a digitial control word in the period of a single clock cycle. An NCO's output frequency can change instantly without the acquisition and lock time delays associated with conventional phase-locked loop synthesizers.
A typical NCO uses a phase accumulator, a phase-to-amplitude converter (PAC), a digital-to-analog converter (DAC), and a bandpass or low pass filter to generate a sinusoidal signal. The purity of the NCO output signal depends in large measure on generating digital amplitude words within the PAC which accurately represent a sampled sine wave.
Most PACs use two or more lookup tables and some associated logic to provide the phase-to-amplitude conversion. The size of the lookup tables may be reduced when certain approximations are made. However, each approximation reduces the PAC size at the expense of amplitude word accuracy. When choosing an NCO design, a tradeoff exists between spectral purity, PAC size and power.
In U.S. Pat. No. 4,486,845, entitled "Numerically Controlled Oscillator Using Quadrant Replication and Function Decomposition," issued Dec. 4, 1984, the size of the PAC is reduced by reducing the amount of data in a lookup table to include fine and coarse values for only the first quadrant of a sine and a cosine wave. The second quadrant sine must be produced from the cosine of the first quadrant and (vice versa) or boundary errors will be produced. From this information and related logic circuity, the remaining quadrants can be calculated. This has reduced the size of the NCO allowing it to fit on one semiconductor chip without affecting amplitude word accuracy. A further reduction in size, however, would make NCO large scale integration in high-speed ECL or gallium arsenide technologies more feasible.